DOCSLIB.ORG

Thermodynamics of Ideal Gases

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thermodynamics of Ideal Gases D Thermodynamics of ideal gases An ideal gas is a nice “laboratory” for understanding the thermodynamics of a fluid with a non-trivial equation of state. In this section we shall recapitulate the conventional thermodynamics of an ideal gas with constant heat capacity. For more extensive treatments, see for example [67, 66]. D.1 Internal energy In section 4.1 we analyzed Bernoulli’s model of a gas consisting of essentially 1 2 non-interacting point-like molecules, and found the pressure p = 3 ½ v where v is the root-mean-square average molecular speed. Using the ideal gas law (4-26) the total molecular kinetic energy contained in an amount M = ½V of the gas becomes, 1 3 3 Mv2 = pV = nRT ; (D-1) 2 2 2 where n = M=Mmol is the number of moles in the gas. The derivation in section 4.1 shows that the factor 3 stems from the three independent translational degrees of freedom available to point-like molecules. The above formula thus expresses 1 that in a mole of a gas there is an internal kinetic energy 2 RT associated with each translational degree of freedom of the point-like molecules. Whereas monatomic gases like argon have spherical molecules and thus only the three translational degrees of freedom, diatomic gases like nitrogen and oxy- Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 662 D. THERMODYNAMICS OF IDEAL GASES gen have stick-like molecules with two extra rotational degrees of freedom or- thogonally to the bridge connecting the atoms, and multiatomic gases like carbon dioxide and methane have the three extra rotational degrees of freedom. Accord- ing to the equipartition theorem of statistical mechanics these degrees of freedom 1 will also carry a kinetic energy 2 RT per mole. Molecules also possess vibrational degrees of freedom that may become excited at high temperatures, but we shall disregard them here. The internal energy of n moles of an ideal gas is defined to be, k U = nRT ; (D-2) 2 where k is the number of molecular degrees of freedom. A general result of thermodynamics (Helmholtz’ theorem [67, p. 154]) guarantees that for an ideal gas U cannot depend on the volume but only on the temperature. Physically a gas may dissociate or even ionize when heated, and thereby change its value of k, but we shall for simplicity assume that k is in fact constant with k = 3 for monatomic, k = 5 for diatomic, and k = 6 for multiatomic gases. For mixtures of gases the number of degrees of freedom is the molar average of the degrees of freedom of the pure components (see problem D.1). D.2 Heat capacity Suppose that we raise the temperature of the gas by ±T without changing its volume. Since no work is performed, and since energy is conserved, the necessary amount of heat is ±Q = ±U = CV ±T where the constant, k C = nR ; (D-3) V 2 is naturally called the heat capacity at constant volume. If instead the pressure of the gas is kept constant while the temperature is raised by ±T , we must also take into account that the volume expands by a certain amount ±V and thereby performs work on the surroundings. The necessary amount of heat is now larger by this work, ±Q = ±U + p±V . Using the ideal gas law (4-26) we have for constant pressure p±V = ±(pV ) = nR±T . Consequently, the amount of heat which must be added per unit of increase in temperature at constant pressure is Cp = CV + nR ; (D-4) called the heat capacity at constant pressure. It is always larger than CV because it includes the work of expansion. Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 D.3. ENTROPY 663 The adiabatic index The dimensionless ratio of the heat capacities, C 2 γ = p = 1 + ; (D-5) CV k is for reasons that will become clear in the following called the adiabatic index. It is customary to express the heat capacities in terms of γ rather than k, 1 γ C = nR ; C = nR : (D-6) V γ ¡ 1 p γ ¡ 1 Given the adiabatic index, all thermodynamic quantities for n moles of an ideal gas are completely determined. The value of the adiabatic index is γ = 5=3 for monatomic gases, γ = 7=5 for diatomic gases, and γ = 4=3 for multiatomic gases. D.3 Entropy When neither the volume nor the pressure are kept constant, the heat that must be added to the system in an infinitesimal process is, ±V ±Q = ±U + p±V = C ±T + nRT : (D-7) V V It is a mathematical fact that there exists no function, Q(T;V ), which has this expression as differential (see problem D.2). It may on the other hand be directly verified (by insertion) that ±Q ±T ±V ±S = = C + nR ; (D-8) T V T V can be integrated to yield a function, S = CV log T + nR log V + const ; (D-9) called the entropy of the amount of ideal gas. Being an integral the entropy is only defined up to an arbitrary constant. The entropy of the gas is, like its energy, an abstract quantity which cannot be directly measured. But since both quantities depend on the measurable thermodynamic quantities, ½, p, and T , that characterize the state of the gas, we can calculate the value of energy and entropy in any state. But why bother to do so at all? The two fundamental laws of thermodynamics The reason is that the two fundamental laws of thermodynamics are formulated in terms of the energy and the entropy. Both laws concern processes that may Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 664 D. THERMODYNAMICS OF IDEAL GASES take place in an isolated system which is not allowed to exchange heat with or perform work on the environment. The First Law states that the energy is unchanged under any process in an V isolated system. This implies that the energy of an open system can only change by exchange of heat or work with the environment. We actually used this law implicitly in deriving the heat capacities and the entropy. ....... The Second Law states that the entropy cannot decrease. In the real world, ......... ..................... V0 ................... the entropy of an isolated system must in fact grow. Only if all the processes .......... ........ taking place in the system are completely reversible at all times, will the entropy stay constant. Reversibility is an ideal which can only be approached by very slow quasistatic processes, consisting of infinitely many infinitesimal reversible steps. Essentially all real-world processes are irreversible to some degree. A compartment of volume V0 inside an isolated box of volume V . Initially, Example D.3.1 (Joule’s expansion experiment): An isolated box of vol- the compartment contains ume V contains an ideal gas in a walled-off compartment of volume V0. When the an ideal gas with vacuum wall is opened, the gas expands into vacuum and fills the full volume V . The box in the remainder of the is completely isolated from the environment, and since the internal energy only de- box. When the wall breaks, the gas expands by itself pends on the temperature, it follows from the First Law that the temperature must to fill the whole box. The be the same before and after the event. The change in entropy then becomes reverse process would entail a decrease in entropy and ∆S = (CV log T + nR log V ) ¡ (CV log T + nR log V0) = nR log(V=V0) never happens by itself. which is evidently positive (because V=V0 > 1). This result agrees with the Second James Prescott Joule (1818- Law, which thus appears to be unnecessary. 1889). English physicist. The strength of the Second Law becomes apparent when we ask the question Gifted experimenter who as of whether the air in the box could ever — perhaps by an unknown process to be the first demonstrated the discovered in the far future — by itself enter the compartment of volume V0, leaving equivalence of mechanical vacuum in the box around. Since such an event would entail a negative change in work and heat, a necessary step on the road to the First entropy which is forbidden by the Second Law, it never happens. Law. Demonstrated (in con- tinuation of earlier experi- ments by Gay-Lussac) that Isentropic processes the irreversible expansion of a gas into vacuum does not Any process in an open system which does not exchange heat with the environ- change its temperature. ment is said to be adiabatic. If the process is furthermore reversible, it follows that ±Q = 0 in each infinitesimal step, so that the ±S = ±Q=T = 0. The entropy (D-9) must in other words stay constant in any reversible, adiabatic process. Such a process is for this reason called isentropic. By means of the adiabatic index (D-5) we may write the entropy (D-9) as, ¡ γ¡1¢ S = CV log TV + const : (D-10) From this it follows that TV γ¡1 = const ; (D-11) for any isentropic process in an ideal gas. Using the ideal gas law to eliminate V » T=p, this may be written equivalently as, T γ p1¡γ = const : (D-12) Copyright °c 1998{2004, Benny Lautrup Revision 7.7, January 22, 2004 D.3. ENTROPY 665 Eliminating instead T » pV , the isentropic condition takes its most common form, p V γ = const : (D-13) Notice that the constants are different in these three equations.
Load more

Recommended publications
  • Entropy: Ideal Gas Processes
    Chapter 19: The Kinec Theory of Gases Thermodynamics = macroscopic picture Gases micro -> macro picture One mole is the number of atoms in 12 g sample Avogadro’s Number of carbon-12 23 -1 C(12)—6 protrons, 6 neutrons and 6 electrons NA=6.02 x 10 mol 12 atomic units of mass assuming mP=mn Another way to do this is to know the mass of one molecule: then So the number of moles n is given by M n=N/N sample A N = N A mmole−mass € Ideal Gas Law Ideal Gases, Ideal Gas Law It was found experimentally that if 1 mole of any gas is placed in containers that have the same volume V and are kept at the same temperature T, approximately all have the same pressure p. The small differences in pressure disappear if lower gas densities are used. Further experiments showed that all low-density gases obey the equation pV = nRT. Here R = 8.31 K/mol ⋅ K and is known as the "gas constant." The equation itself is known as the "ideal gas law." The constant R can be expressed -23 as R = kNA . Here k is called the Boltzmann constant and is equal to 1.38 × 10 J/K. N If we substitute R as well as n = in the ideal gas law we get the equivalent form: NA pV = NkT. Here N is the number of molecules in the gas. The behavior of all real gases approaches that of an ideal gas at low enough densities. Low densitiens m= enumberans tha oft t hemoles gas molecul es are fa Nr e=nough number apa ofr tparticles that the y do not interact with one another, but only with the walls of the gas container.
    [Show full text]
  • IB Questionbank
    Topic 3 Past Paper [94 marks] This question is about thermal energy transfer. A hot piece of iron is placed into a container of cold water. After a time the iron and water reach thermal equilibrium. The heat capacity of the container is negligible. specific heat capacity. [2 marks] 1a. Define Markscheme the energy required to change the temperature (of a substance) by 1K/°C/unit degree; of mass 1 kg / per unit mass; [5 marks] 1b. The following data are available. Mass of water = 0.35 kg Mass of iron = 0.58 kg Specific heat capacity of water = 4200 J kg–1K–1 Initial temperature of water = 20°C Final temperature of water = 44°C Initial temperature of iron = 180°C (i) Determine the specific heat capacity of iron. (ii) Explain why the value calculated in (b)(i) is likely to be different from the accepted value. Markscheme (i) use of mcΔT; 0.58×c×[180-44]=0.35×4200×[44-20]; c=447Jkg-1K-1≈450Jkg-1K-1; (ii) energy would be given off to surroundings/environment / energy would be absorbed by container / energy would be given off through vaporization of water; hence final temperature would be less; hence measured value of (specific) heat capacity (of iron) would be higher; This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves. Part 1 Ideal gases and specific heat capacity State assumptions of the kinetic model of an ideal gas. [2 marks] 2a. two Markscheme point molecules / negligible volume; no forces between molecules except during contact; motion/distribution is random; elastic collisions / no energy lost; obey Newton’s laws of motion; collision in zero time; gravity is ignored; [4 marks] 2b.
    [Show full text]
  • 5.5 ENTROPY CHANGES of an IDEAL GAS for One Mole Or a Unit Mass of Fluid Undergoing a Mechanically Reversible Process in a Closed System, the First Law, Eq
    Thermodynamic Third class Dr. Arkan J. Hadi 5.5 ENTROPY CHANGES OF AN IDEAL GAS For one mole or a unit mass of fluid undergoing a mechanically reversible process in a closed system, the first law, Eq. (2.8), becomes: Differentiation of the defining equation for enthalpy, H = U + PV, yields: Eliminating dU gives: For an ideal gas, dH = and V = RT/ P. With these substitutions and then division by T, As a result of Eq. (5.11), this becomes: where S is the molar entropy of an ideal gas. Integration from an initial state at conditions To and Po to a final state at conditions T and P gives: Although derived for a mechanically reversible process, this equation relates properties only, and is independent of the process causing the change of state. It is therefore a general equation for the calculation of entropy changes of an ideal gas. 1 Thermodynamic Third class Dr. Arkan J. Hadi 5.6 MATHEMATICAL STATEMENT OF THE SECOND LAW Consider two heat reservoirs, one at temperature TH and a second at the lower temperature Tc. Let a quantity of heat | | be transferred from the hotter to the cooler reservoir. The entropy changes of the reservoirs at TH and at Tc are: These two entropy changes are added to give: Since TH > Tc, the total entropy change as a result of this irreversible process is positive. Also, ΔStotal becomes smaller as the difference TH - TC gets smaller. When TH is only infinitesimally higher than Tc, the heat transfer is reversible, and ΔStotal approaches zero. Thus for the process of irreversible heat transfer, ΔStotal is always positive, approaching zero as the process becomes reversible.
    [Show full text]
  • Chapter 3 3.4-2 the Compressibility Factor Equation of State
    Chapter 3 3.4-2 The Compressibility Factor Equation of State The dimensionless compressibility factor, Z, for a gaseous species is defined as the ratio pv Z = (3.4-1) RT If the gas behaves ideally Z = 1. The extent to which Z differs from 1 is a measure of the extent to which the gas is behaving nonideally. The compressibility can be determined from experimental data where Z is plotted versus a dimensionless reduced pressure pR and reduced temperature TR, defined as pR = p/pc and TR = T/Tc In these expressions, pc and Tc denote the critical pressure and temperature, respectively. A generalized compressibility chart of the form Z = f(pR, TR) is shown in Figure 3.4-1 for 10 different gases. The solid lines represent the best curves fitted to the data. Figure 3.4-1 Generalized compressibility chart for various gases10. It can be seen from Figure 3.4-1 that the value of Z tends to unity for all temperatures as pressure approach zero and Z also approaches unity for all pressure at very high temperature. If the p, v, and T data are available in table format or computer software then you should not use the generalized compressibility chart to evaluate p, v, and T since using Z is just another approximation to the real data. 10 Moran, M. J. and Shapiro H. N., Fundamentals of Engineering Thermodynamics, Wiley, 2008, pg. 112 3-19 Example 3.4-2 ---------------------------------------------------------------------------------- A closed, rigid tank filled with water vapor, initially at 20 MPa, 520oC, is cooled until its temperature reaches 400oC.
    [Show full text]
  • The Discovery of Thermodynamics
    Philosophical Magazine ISSN: 1478-6435 (Print) 1478-6443 (Online) Journal homepage: https://www.tandfonline.com/loi/tphm20 The discovery of thermodynamics Peter Weinberger To cite this article: Peter Weinberger (2013) The discovery of thermodynamics, Philosophical Magazine, 93:20, 2576-2612, DOI: 10.1080/14786435.2013.784402 To link to this article: https://doi.org/10.1080/14786435.2013.784402 Published online: 09 Apr 2013. Submit your article to this journal Article views: 658 Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tphm20 Philosophical Magazine, 2013 Vol. 93, No. 20, 2576–2612, http://dx.doi.org/10.1080/14786435.2013.784402 COMMENTARY The discovery of thermodynamics Peter Weinberger∗ Center for Computational Nanoscience, Seilerstätte 10/21, A1010 Vienna, Austria (Received 21 December 2012; final version received 6 March 2013) Based on the idea that a scientific journal is also an “agora” (Greek: market place) for the exchange of ideas and scientific concepts, the history of thermodynamics between 1800 and 1910 as documented in the Philosophical Magazine Archives is uncovered. Famous scientists such as Joule, Thomson (Lord Kelvin), Clau- sius, Maxwell or Boltzmann shared this forum. Not always in the most friendly manner. It is interesting to find out, how difficult it was to describe in a scientific (mathematical) language a phenomenon like “heat”, to see, how long it took to arrive at one of the fundamental principles in physics: entropy. Scientific progress started from the simple rule of Boyle and Mariotte dating from the late eighteenth century and arrived in the twentieth century with the concept of probabilities.
    [Show full text]
  • Module P7.4 Specific Heat, Latent Heat and Entropy
    FLEXIBLE LEARNING APPROACH TO PHYSICS Module P7.4 Specific heat, latent heat and entropy 1 Opening items 4 PVT-surfaces and changes of phase 1.1 Module introduction 4.1 The critical point 1.2 Fast track questions 4.2 The triple point 1.3 Ready to study? 4.3 The Clausius–Clapeyron equation 2 Heating solids and liquids 5 Entropy and the second law of thermodynamics 2.1 Heat, work and internal energy 5.1 The second law of thermodynamics 2.2 Changes of temperature: specific heat 5.2 Entropy: a function of state 2.3 Changes of phase: latent heat 5.3 The principle of entropy increase 2.4 Measuring specific heats and latent heats 5.4 The irreversibility of nature 3 Heating gases 6 Closing items 3.1 Ideal gases 6.1 Module summary 3.2 Principal specific heats: monatomic ideal gases 6.2 Achievements 3.3 Principal specific heats: other gases 6.3 Exit test 3.4 Isothermal and adiabatic processes Exit module FLAP P7.4 Specific heat, latent heat and entropy COPYRIGHT © 1998 THE OPEN UNIVERSITY S570 V1.1 1 Opening items 1.1 Module introduction What happens when a substance is heated? Its temperature may rise; it may melt or evaporate; it may expand and do work1—1the net effect of the heating depends on the conditions under which the heating takes place. In this module we discuss the heating of solids, liquids and gases under a variety of conditions. We also look more generally at the problem of converting heat into useful work, and the related issue of the irreversibility of many natural processes.
    [Show full text]
  • Real Gases – As Opposed to a Perfect Or Ideal Gas – Exhibit Properties That Cannot Be Explained Entirely Using the Ideal Gas Law
    Basic principle II Second class Dr. Arkan Jasim Hadi 1. Real gas Real gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behavior of real gases, the following must be taken into account: compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects; Issues with molecular dissociation and elementary reactions with variable composition. Critical state and Reduced conditions Critical point: The point at highest temp. (Tc) and Pressure (Pc) at which a pure chemical species can exist in vapour/liquid equilibrium. The point critical is the point at which the liquid and vapour phases are not distinguishable; because of the liquid and vapour having same properties. Reduced properties of a fluid are a set of state variables normalized by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states The reduced pressure is defined as its actual pressure divided by its critical pressure : The reduced temperature of a fluid is its actual temperature, divided by its critical temperature: The reduced specific volume ") of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature: This property is useful when the specific volume and either temperature or pressure are known, in which case the missing third property can be computed directly. 1 Basic principle II Second class Dr. Arkan Jasim Hadi In Kay's method, pseudocritical values for mixtures of gases are calculated on the assumption that each component in the mixture contributes to the pseudocritical value in the same proportion as the mol fraction of that component in the gas.
    [Show full text]
  • Problem Set 8 Due: Thursday, June 6, 2019
    Physics 12c: Problem Set 8 Due: Thursday, June 6, 2019 1. Problem 2 in chapter 9 of Kittel and Kroemer. 2. Latent heat of melting Consider a substance which can exist in either one of two phases, labeled A and B. If the number of molecules is N, the heat capacity of the A phase at temperature τ is 3 CA = Nατ ; (1) while the heat capacity of the B phase is CB = Nβτ: (2) (a) Assuming the entropy is zero at zero temperature, find the entropies σA; σB of the two phases at temperature τ. (b) Suppose that, for both the A phase and the B phase, the internal energy is U0 = N0 at zero temperature. Find the internal energies UA;UB of the two phases at temperature τ. (c) Using the thermodynamic identity dU = τdσ+µdN, find the chemical potentials µA; µB of the two phases, expressed as functions of τ. (d) Which phase is favored at low temperature? At what \melting" temperature τm does a transition occur to the other phase? (e) At the melting temperature, how much heat must be added to transform the low-temperature phase to the high-temperature phase? 3. Latent heat of BEC Bose-Einstein condensation of an ideal gas may be regarded as a sort of first-order phase transition, where the two coexisting phases are the “liquified” condensate (the particles in the ground orbital) and the \normal" gas (the particles in excited or- bitals). The purpose of this problem is to calculate the latent heat of this transition. Assume that the particles are spinless bosons with mass m.
    [Show full text]
  • Thermodynamic Temperature
    Thermodynamic temperature Thermodynamic temperature is the absolute measure 1 Overview of temperature and is one of the principal parameters of thermodynamics. Temperature is a measure of the random submicroscopic Thermodynamic temperature is defined by the third law motions and vibrations of the particle constituents of of thermodynamics in which the theoretically lowest tem- matter. These motions comprise the internal energy of perature is the null or zero point. At this point, absolute a substance. More specifically, the thermodynamic tem- zero, the particle constituents of matter have minimal perature of any bulk quantity of matter is the measure motion and can become no colder.[1][2] In the quantum- of the average kinetic energy per classical (i.e., non- mechanical description, matter at absolute zero is in its quantum) degree of freedom of its constituent particles. ground state, which is its state of lowest energy. Thermo- “Translational motions” are almost always in the classical dynamic temperature is often also called absolute tem- regime. Translational motions are ordinary, whole-body perature, for two reasons: one, proposed by Kelvin, that movements in three-dimensional space in which particles it does not depend on the properties of a particular mate- move about and exchange energy in collisions. Figure 1 rial; two that it refers to an absolute zero according to the below shows translational motion in gases; Figure 4 be- properties of the ideal gas. low shows translational motion in solids. Thermodynamic temperature’s null point, absolute zero, is the temperature The International System of Units specifies a particular at which the particle constituents of matter are as close as scale for thermodynamic temperature.
    [Show full text]
  • • Introduction to Thermodynamics • Temperature Scales, Absolute Zero • Phase Changes, Equilibrium, Diagram Interlude
    Lecture 9 • Introduction to thermodynamics • Temperature scales, absolute zero • Phase changes, equilibrium, diagram Interlude Quiz (Thursday, March 5) • Chapter 21 1st mid-term (Tuesday, March 10) • Chapters 14, 15 (except 15.6), 20 and 21 • diverse topics: start preparing now Thermodynamics (Chs. 16-19) • Next few weeks: transformation of energy from one form to another: e.g. engines convert fuel energy into mechanical; living organisms convert chemical energy of food into kinetic... macroscopic systems instead of particles; temperature (T), pressure (p)...instead of position, velocity... How do pressure, temperature change or work done by engines related to fuel energy used? macro/micro connection: T related to motion of atoms...2nd law... ultimate goal: how heat engines convert heat energy to work • This week bulk properties (T, p) phases of matter; phase changes start micro/macro connection • Today: 3 phases of matter; mass... Solids, Liquids and Gases change between liquild/solid or liquid/gas: phase change • Solids rigid: atoms vibrate, but not free to move; incompressible (atoms as close as can be); crystal (arranged in periodic arrray) or amorphous (random) • Liquids incompressible, but flows/fits shape of container: molecules can slide around each other, but can’t get far apart • Gases freely moving molecules...till collide with each other/wall compressible (lot of space...) State variables parameters describing macroscopic systems e.g. • M mass (M), density (ρ ), p, T...related: e.g., ρ = V change state by changing variables:
    [Show full text]
  • Chem 322, Physical Chemistry II: Lecture Notes
    Chem 322, Physical Chemistry II: Lecture notes M. Kuno December 20, 2012 2 Contents 1 Preface 1 2 Revision history 3 3 Introduction 5 4 Relevant Reading in McQuarrie 9 5 Summary of common equations 11 6 Summary of common symbols 13 7 Units 15 8 Math interlude 21 9 Thermo definitions 35 10 Equation of state: Ideal gases 37 11 Equation of state: Real gases 47 12 Equation of state: Condensed phases 55 13 First law of thermodynamics 59 14 Heat capacities, internal energy and enthalpy 79 15 Thermochemistry 111 16 Entropy and the 2nd and 3rd Laws of Thermodynamics 123 i ii CONTENTS 17 Free energy (Helmholtz and Gibbs) 159 18 The fundamental equations of thermodynamics 179 19 Application of Free Energy to Phase Transitions 187 20 Mixtures 197 21 Equilibrium 223 22 Recap 257 23 Kinetics 263 Chapter 1 Preface What is the first law of thermodynamics? You do not talk about thermodynamics What is the second law of thermodynamics? You do not talk about thermodynamics 1 2 CHAPTER 1. PREFACE Chapter 2 Revision history 2/05: Original build 11/07: Corrected all typos caught to date and added some more material 1/08: Added more stuff and demos. Made the equilibrium section more pedagogical. 5/08: Caught more typos and made appropriate fixes to some nomenclature mistakes. 12/11: Started the next round of text changes and error corrections since I’m teaching this class again in spring 2012. Woah! I caught a whole bunch of problems that were present in the last version. It makes you wonder what I was thinking.
    [Show full text]
  • Physical Chemistry I
    Physical Chemistry I Andrew Rosen August 19, 2013 Contents 1 Thermodynamics 5 1.1 Thermodynamic Systems and Properties . .5 1.1.1 Systems vs. Surroundings . .5 1.1.2 Types of Walls . .5 1.1.3 Equilibrium . .5 1.1.4 Thermodynamic Properties . .5 1.2 Temperature . .6 1.3 The Mole . .6 1.4 Ideal Gases . .6 1.4.1 Boyle’s and Charles’ Laws . .6 1.4.2 Ideal Gas Equation . .7 1.5 Equations of State . .7 2 The First Law of Thermodynamics 7 2.1 Classical Mechanics . .7 2.2 P-V Work . .8 2.3 Heat and The First Law of Thermodynamics . .8 2.4 Enthalpy and Heat Capacity . .9 2.5 The Joule and Joule-Thomson Experiments . .9 2.6 The Perfect Gas . 10 2.7 How to Find Pressure-Volume Work . 10 2.7.1 Non-Ideal Gas (Van der Waals Gas) . 10 2.7.2 Ideal Gas . 10 2.7.3 Reversible Adiabatic Process in a Perfect Gas . 11 2.8 Summary of Calculating First Law Quantities . 11 2.8.1 Constant Pressure (Isobaric) Heating . 11 2.8.2 Constant Volume (Isochoric) Heating . 11 2.8.3 Reversible Isothermal Process in a Perfect Gas . 12 2.8.4 Reversible Adiabatic Process in a Perfect Gas . 12 2.8.5 Adiabatic Expansion of a Perfect Gas into a Vacuum . 12 2.8.6 Reversible Phase Change at Constant T and P ...................... 12 2.9 Molecular Modes of Energy Storage . 12 2.9.1 Degrees of Freedom . 12 1 2.9.2 Classical Mechanics .
    [Show full text]